Multiple zeta values
Arborified multiple zeta values
... of multiple zeta values first appears in 1981 in a preprint of Jean Ecalle under the name ”moule ζ • < ”, in the context of resurgence theory in complex analysis [13, Page 429], together with its ...
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Renormalisation group for multiple zeta values
... Calculating multiple zeta values at arguments of any sign in a way that is com- patible with both the quasi-shuffle product as well as meromorphic continuation, is commonly referred to as the ...
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From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
... elliptic multiple polylogarithms (as defined in ...special values of infinite sums of single-valued multiple polylogarithms, and these infinite sums are proposed in the reference to be a ...
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Unfolding the double shuffle structure of q-multiple zeta values
... We started to explore how the resulting double q-shuffle relations may be used to express the δ- derivation terms in (7) as linear combinations of qMZVs. The simplest example yields for a = 2 = b: δ¯z q (2) = 4¯z q (3, ...
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Arithmetic of values of L-functions and generalized multiple zeta values over number fields
... classical Zeta Values Classically, multiple Zeta values(MZVs) are the periods of mixed Tate motives, namely the MZVs are iterated integrals on P 1 ∖ ...
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A note on certain alternating series involving zeta and multiple zeta values
... In this section, we consider a more general class of series of the previous type replacing zeta values with certain multiple zeta values. We prove our formula (3) and deduce some ...
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Renormalisation of q-Regularised Multiple Zeta Values
... of multiple zeta ...q-multiple zeta values to negative integers. Renormalised multiple zeta values satisfying the quasi-shuffle product are obtained using an Hopf ...
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Duality and (q-)multiple zeta values
... restrict this construction to non-negative arguments in the context of the quasi-shuffle product, then the coproduct of convergent words coincides with the coproduct obtained from the duality construction. As a result ...
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Multiple zeta functions and polylogarithms over global function fields
... Abstract. In [36], Thakur defines function field analogs of the classical mul- tiple zeta function, namely, ζd (F q [T ]; s 1 , . . . , s d) and ζd(K; s 1 , . . . , s d), where K is a global function field. Star ...
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Nested sums of symbols and renormalised multiple zeta functions
... Hurwitz multiple zeta values, which converge for Re(s 1 + · · · + s m ) > nm for any m ∈ {1, ...dimensional multiple zeta values with the supremum norm replaced by the ...
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A sum-shuffle formula for zeta values in Tate algebras
... Theorem 2.5. For all Σ ⊂ N ∗ a finite subset, the Fp -subvector space of T Σ (K ∞ ) generated by the multiple zeta values (2.1) is an F p -algebra. 3. sum-shuffle relations We follow the main idea of ...
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Generating functions for multiple zeta star values
... Introduction Multiple Euler sums and multiple zeta values (MZVs) have been of in- terest for mathematicians and physicists for more than two ...ple zeta star values in general ...
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Motivic zeta functions of motives
... ccsd-00080469, version 1 - 17 Jun 2006 BRUNO KAHN Introduction Let M be a tensor category with coefficients in a field K of character- istic 0, that is, a K-linear pseudo-abelian symmetric monoidal category such that ...
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Sur une somme des cotangentes associées à la fonction zeta d'Estermann
... Et on souhaite que la fonction soit calculable en pratique (voir [?]) : la fonction ζ de Riemann (Voir[10] et [8]), a été introduite pour fournir la position des nombres premiers : En fa[r] ...
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Laurent expansion of harmonic zeta functions
... C m−p can then be determined by the same method used in section 2.1. References [1] T. Amdeberhan, O. Espinosa, I. Gonzalez, M. Harrison, V. H. Moll, and A. Straub, Ramanujan’s Master Theorem, Ramanujan J. 29 (2012), ...
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Twisted characteristic $p$ zeta functions
... Notices no. 12 (2009), 2318-2346. [40] D. Thakur, Shuffle relations for function field multizeta values, International Mathematics Research Notices no. 11 (2010), 1973-1980. Universit´ e de Caen Normandie, ...
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Fonction $\zeta $ de Carlitz et automates
... Il suffit alors de comparer les indices des plus grands termes non nuls de.. chacune de deux telles décompositions.[r] ...
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On systolic zeta functions
... Theorem 3.2. Let P be a combinatorial graph with first Betti number b, and let V = Vol(B st ) be the volume of the unit ball of the stable norm in H 1 (P, R). Then the stable zeta function ζ st (z) of the graph P ...
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Zeta Pup variability revisited
... Zeta Pup variability revisited Yaël Nazé (FNRS/Univ. of Liège, Belgium), Tahina Ramiaramanantsoa (Univ. of Montréal, Canada), Ian R. Stevens (Univ. of Birmingham, UK), Ian D. Howarth (UCL, UK), and Anthony F.J. ...
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A peptide-level multiple imputation strategy accounting for the different natures of missing values in proteomics data
... Assumption 2 (Peptide-wise independence). The complete intensity values of peptides are independently distributed in each sample. Justification: At first look, Ass. 2 may seem inadequate: it could be nat- urally ...
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